Rasch with lme4

2009/6/9 David Duffy <David.Duffy at qimr.edu.au>

Aside from Reinhold's comment, which is not a showstopper (you could bootstrap etc), they are quite different models. In the first model, the estimated IQ-extraversion correlation is disattenuated for measurement error -- the equivalent SEMs are something like (I think ;)):


IQ <-----> E ?v. ? E
| \ ? ? ? ? ? ? ? ?| \
v ?v ? ? ? ? ? ? ? v ?v
i1 i2 ? ? ? ? ? ? ?i1 i2
? ? ? ? ? ? ? ? ? ^ ?^
? ? ? ? ? ? ? ? ? | /
? ? ? ? ? ? ? ? ? IQ

I am not convinced the second SEM model correclty represents the
second lme model. In the sem model the effect of IQ on y seems to be
conditional on the effect of Extraversion, and vice versa. However,
the fixed effect of extraversion on y does not seem to change
tremendously whether a random effect of subjects is included in the
model or not. I think this is because 'IQ' is only represented by a
random effect in the multilevel model, and the sem model seems to
imply a fixed effect.